History of Mathematics for Teachers of Grades 9-12

Date	CLASSWORK AND HOMEWORK Work is due at the beginning of class unless otherwise noted!
July 17 - Mon	Classwork Number Theory Registration Discuss scheduling of course and syllabus What history have you covered in your own classroom? and Introductions Why history in the classroom? NCTM Standards on history. Hand out Who? How? What? A Strategy for Using History to Teach Mathematics Hand out selections from Math Through the Ages, History of numbers, primes and the Sieve of Eratosthenes Euclid's Book IX Prop 20 Ancient Fractions and Babylonian Yale tablet. Triangle Measuring, irrationality of sqrt(2) and history. Cantor diagonalization DodgeBall worksheet, Dr. Sarah's Cantor worksheet. Move to the computer lab. Intro to web searching and sum of cubes worksheet. Prepare to present your findings. Reflection: discuss effects of representations of mathematicians NCTM Standards in grades 9-12 for Number and Operations Standard. Intro to the CD. Search for activities related to these standards and prepare to present your findings. Homework for Tuesday History of numbers worksheet homework, linear equations worksheet homework, and begin working on the Reflective Journal and CD assignments.
July 18 - Tues	Classwork Algebra Linear equations: Egypt Rhind Papyrus, Babylon, China: Egyptian Multiplication/Division The origin of algebraic manipulation via Linear Equations in One Unknown - Islamic Method worksheet from the CD Linear Eqs 32-33. Chinese method of double false position of solving two linear equations with two unknowns via Chinese Problems worksheet from the CD NegNums 42-44. System of Three Linear Equations - The Chinese Solution from Algebra Activities from Many Cultures Multicultural Origin of the Quadratic Formula worksheet from Algebra Activities from Many Cultures History of Plimpton 322 via web search (Plimpton 322) Brief history of the Pythagorean Theorem via a web search (history of the pythagorean theorem): site and site Additional History of Math sites: MacTutor History of Mathematics Archive (Pythagorean site:www-groups.dcs.st-and.ac.uk/) Mathematicians of the African Diaspora Convergence: where mathematics, history and teaching interact Scarecrow's Theorem Slide 1 Slide 2 Copyright Slide Cubic equations: Europe - leading to sqrt(-1) Solutions to the quintic Maple demo and fictional account of Galois Begin Wednesday's classwork. Homework for Wednesday Choose an NCTM standard related to algebra or geometry. Write down that standard. Then find an activity related to that standard that is not from our CD. You may find an activity in one of the books or from a web search. Specify how the activity relates to the standard that you chose. Continue working on the Reflective Journal and CD assignments. Your CD project topic must be approved by Dr. Sarah by Wednesday. Provide the Chapter and page number in addition to the title of the activity.
July 19 - Wed	Classwork Geometry What is geometry? Groups discuss and come back together. Brief history of early geometry knowledge including the Babylonians, Egyptians, Greeks (Thales, Pythagoras, Plato, Euclid), Chinese, and Africans. Mention the Timeline for Geometry: Multicultural Highpoints from Geometry Activities from Many Cultures Skim LAV 6 section of the CD on Origins of Length, Area, and Volume Measurement Mention CD LAV 80 on Thales' Shadow Measurement Activity Mention CD Trig 80 and LAV 88 on Eratosthenes' Size of the Earth and Trig 112 on Al-Biruni's Calculation on the Size of the Earth History of Euclid's elements including Euclid's 5th postulate (prop 29 and later). Sum of the Angles in a Triangle: Write out Proposition 32 in modern language. Discuss Euclid's historical proof, paper folding, and then an Intro to Geometric Constructions via a construction in Sketchpad. Dr. Sarah models the construction. Discuss the history (attributed to Pythagoras), and compare and contrast the activities, discussing the benefits and difficulties with using them in various classes. Then the group goes to the computer lab to try the Sketchpad construction. Pythagorean Theorem: Discuss the Yale tablet and Babylonian Pythagorean knowledge. Discuss the history of Euclid Book 1 Proposition 47 and of it's importance in measurement. Discuss Sketchpad demonstrations of the Pythagorean Theorem. From Sketchpad, under File/open, go to Desktop/205Math(yourcomputersnumber)/Applications/Sketchpad/ Samples/Sketches/Geometry/Pythagoras.gsp Go through Behold Pythagoras! and Puzzled Pythagoras. Return to the classroom. (Highlight Euclid's Proof), discuss the historical differences in proofs, and then Dr. Sarah's models the Pythagorean Theorem in Sketchpad. Mention CD activities LAV 124 Pythagorean Theorem, LAV 130 Practical Pythagorean Theorem, Geom 103 Pythagorean Project Hand out A Chinese Proof of the Theorem from Geometry Activities from Many Cultures in order to complement the Sketchpad Behold Pythagoras! activity Compare and contrast the methods used in the classroom. Non-Euclidean Geometry: Dynamic Geometry activities on the sphere and hyperbolic Poincare disk Walter Fendt's Java Applet and the sum of the angles and the Pythagorean Theorem Escher worksheet Sketchpad Hyperbolic Sum of Angles Sketchpad Hyperbolic Pythagorean Theorem Mention built in hyperbolic Sketchpad exploration and Brad Findell's Elliptic/Spherical Toolkit for Sketchpad Why Study Hyperbolic Geometry? and a brief history of non-Euclidean geometry. Hand out Explorers of Non-Euclidean Geometry from Geometry Activities from Many Cultures Mention CD Trig 151 on Spherical Trig Read through the Shape of the Universe and discuss Return to the computer lab. History of modern geometry via web searches. Return to the classroom. A brief history of geometry education. Brief history of the connections and differences between algebra and geometry The Proof video Mention the teacher's guide available at NOVA Online Powers of twelve activity and the related DXC history and history of writers in the classroom Homework for Thursday Complete the CD assignment.
July 20 - Thur	Classwork CD presentations and Precursors to Calculus Finish up classwork from Wednesday CD presentations Ben Franklin's Will Begin calculus: Discussion based on The Paradoxes of Zeno from From Agnesi to Zeno Archimedes: Archimedes and pi via inscribed and circumscribed polygons. Hand out the Hypatia worksheet Examine the related NOVA website applet Archimedes finding the area of a parabola in terms of the area of a triangle and the quadrature of a parabola Applications of series: history of the approximation of Pi and the number of known digits of Pi. Apu and pi in Maple, and search for the world record on the number of digits. Discuss Bailey and Borwein's series. Archimedes computation of the area of a sphere as four times the length of the great circle via oranges Archimedes and the volume of a sphere. Read and discuss Measuring Volumes The Archimedes Palimpsest Analytic Geometry Notes Create timeline - include names, year, and accomplishments Homework for Friday Study for Assessment. Complete the Reflective Journal Assignment.
July 21 - Fri	Classwork Calculus Notes Barrow, Newton, and Leibniz Earliest Uses of Various Mathematical Symbols The spread of calculus: Agnesi and the witch of Agnesi Analytical Institutions Witch. Mention Curve Bank and History Sites Rigor in calculus and modern analysis Revisit discussion of representations of mathematicians. Issues in current research on history of math and ethnomathematics and web searches CD presentation reflections Homework for Saturday July 29th Work on the final project.
July 29 - Sat	Final project due as a word-processed document or a PDF file, sent as an attachment in an email to [email protected]. Libby Davis: Golden Ratio Appendix Janie Fossett: Logic and Venn Diagrams Becky Frawley: Fibonacci Sequence Kara Hicks: The Variable X Rebekkah Niles: Negative Numbers Chinese Shang Numerals Guide Teacher's Example for Overhead Teacher's Answer Guide for Overhead Blank Shang Numeral Practice Sheets Negative Numbers Practice Sheet Negative Numbers Practice Sheet Answers